Results 1 to 5 of 5

Math Help - Finding values between two mins or two maxes

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    2

    Finding values between two mins or two maxes

    Hello,
    I am trying to find the value between two maxes/two mins. I just need to see how long a wavelength is.
    I have the equation. It is a cos function: 2 + 2.5cos(2pi*60*t).
    So, In order to find all maxes and mins, I will derive the above function, and I get:
    -sin(2pi*60*t)

    I need to set this to zero to find the x values of the max and mins. This is where the problem comes in. I have forgotten how to solve for this:
    0 = -sin(2pi*60*t)

    I do the inverse of sin of both sides and get this:
    0 = -(2pi*60*t)
    What is the inverse sin of 0? It's a large range correct?
    The next max or min can be found by doing:
    pi = -(2pi*60*t) correct?

    I tried that, and I get 0 and 1/30, which is def. not the interval between a max and a min. I was going to find the time between a max and a min and multiply by two to find the length of the wavelength. When I calculated this eq. into my graphing calculator, 1/15 is def. not the distance of a wavelength.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Educated's Avatar
    Joined
    Aug 2010
    From
    New Zealand
    Posts
    418
    Thanks
    11
    The derivative is wrong.

    \frac{d}{dt}(2 + 2.5cos(2 \pi \cdot 60\cdot t)) \ne -sin(2pi\cdot 60\cdot t)

    Since the t variable is inside the cosine, you would have to use the chain rule to differentiate it.

    Chain rule: \frac{dy}{dx}=\frac{dy}{du} \cdot \frac{du}{dx}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,325
    Thanks
    1295
    You don't really need to know the derivative of "max" or "min" to find the wavelength.

    You know (I hope!) that cos(x) has period (wavelength) 2\pi- that is, one wave starts at x= 0 and ends at x= 2\pi. That means that, for this function the wave starts where 2\pi (60t)= 0, or t= 0, and ends where 2\pi (60t)= 2\pi or t= \frac{1}{60}. This function has a period (wavelength) of \frac{1}{60}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    2
    When I graph the function, I am getting x=~ 6 for the length of the wavelength and not 1/60.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member Educated's Avatar
    Joined
    Aug 2010
    From
    New Zealand
    Posts
    418
    Thanks
    11
    How are you graphing it? By hand? Graphical calculator? Computer program?

    Here's a graph by Wolfram|Alpha of the equation: Wolfram|Alpha, plot[2 + 2.5cos(2pi*60*t)]

    Are you graphing it in degrees or radians?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Need help with mins and maxes.
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 28th 2010, 08:58 PM
  2. calc 3, maxes and mins. quick question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 21st 2009, 04:54 PM
  3. calc 3, local maxes and mins
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 16th 2009, 04:18 PM
  4. Critical values and max/mins
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 11th 2009, 02:36 PM
  5. Mins and maxes
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 12th 2009, 07:33 PM

Search Tags


/mathhelpforum @mathhelpforum